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Considerations in Source Estimation of the P3 Source estimation Halgren E. Considerations in Source Estimation of the P3. In: Ikeda I, Inoue Y, eds. Event-related Potentials in Patients with Epilepsy: from Current State to Future Prospects. Paris: John Libbey Eurotext 2008: 71-87. Considerations in Source Estimation of the P3 Eric Halgren, Ph.D. Multimodal Imaging Laboratory Departments of Radiology, Neurosciences and Psychiatry, University of California at San Diego Abstract It is not possible to localize the cerebral structures that generate the P3 from non-invasive recordings. In addition to inherent ambiguities in source localization, many generators that are active during the P3 do not propagate to the scalp and thus would remain invisible to even perfect inverse solutions. Furthermore, scalp recordings are not directly informative with regard to underlying neural processes. In theory, fMRI could help distinguish between alternative P3 generators, but in practice, its utility may be limited. Recordings directly within the brain are limited by incomplete sampling and possible pathology. However, they are the only unambiguous means to demonstrate local generation of potentials which overlap in time with the scalp P3 and possess similar cognitive correlates. Decreases in scalp P3 after brain lesions suggest which structures might contribute directly to the scalp P3, but post-lesion decreases can also be due to disruption of antecedent calculations. Despite these considerations, and remaining dissociations, there is increasing convergence in the distribution of generator structures inferred from different methods. However, bringing the P3s and the cognitive states that they embody into mechanistic neuroscience requires going beyond the localization of generating structures to identifying generating synapses, channels and circuits. key words: P300, event-related potentials, cortex, humans, inverse problem, generators, thalamus, slow oscillation, sleep spindle Even a perfect inverse solution cannot localize what it does not see It is impossible to unambiguously localize the structures generating the P3 from extracranial recordings for two fundamental reasons that are inherent in the biophysics of EEG and MEG, and can never be overcome by advances in analysis techniques. First, the inverse problem is ill-posed: there are an infinite number of cortical activation patterns that could result in any recorded scalp-P3 topography. Second, most of the brain generators active during the P3 do not propagate to the scalp to produce a recordable potential due to spatiotemporal cancellation. Fortunately, under some circumstances, intracranial EEG (iEEG) recordings can unambiguously localize P3 generators. Such recordings have made it clear that the P3 actually refers to several states, with different generating structures and evoking circumstances. These studies, reviewed in the companion chapter by Halgren in this volume, serve as a touchstone for evaluating the non-invasive techniques. Neural processes generating EEG and MEG The underlying P3 process can be measured with a variety of techniques, each of which can provide complementary insights. EEG, MEG and the blood oxygenation level dependent (BOLD) response measured with functional MRI are all closely related to synaptic transmission and transmembrane currents (fig. 1). Ionic concentration gradients act as batteries, driving current actively across the membrane, and drawing it from, or pushing it into, the intracellular and extracellular spaces. Aligned intracellular currents are thought to comprise the main generators of MEG [1], whereas aligned extracellular currents are measured as EEG [2]. The intracellular and extracellular currents are equal and passive, and result directly from the same active current flows across neuronal membranes. Consequently, the EEG and MEG share the same active generators but propagate differently to their respective sensors. Thus, they provide complementary localizing information [3,4]. BOLD functions to support the energy needs of the brain, and in primates these are mainly related to synaptic processes and consequent currents [5]. This is the fundamental reason to expect that EEG and MEG measures of the P3 would be highly similar to each other, and at least partially share a generating substrate with the BOLD response in the same task. However, there are also many ways in which these measures could be dissociated, which we shall consider below. 1 Source estimation On the one hand, generation of the EEG (and thus event-related averages of the EEG, and thus the scalp-P3) is very simple: active currents flow across cell membranes in the brain, and these currents then flow through the extracellular space, thus producing potential differences between electrodes at different locations on the scalp. On the other hand, there are many kinds of active currents in the brain, each of which has its own biological context and function [6]. The spatial arrangement of these currents and the paths they take are incredibly complex, as is the spatiotemporal choreography of their activation. Fortunately, biophysical considerations applied to the biology of these currents allow one to understand which of them are likely to contribute to the EEG. In most cases the same considerations apply equally to MEG and they will be discussed together. Action potentials Action potentials contribute little to the M/EEG signal for several reasons [7]. First, the action potential is organized as a central current sink surrounded by sources. Current crosses the axonal membrane behind the active sink to restore its resting potential. Current is drawn from in front of the spike to supply charge to the active sink. Consequently the action potential is equivalent to a quadripole which decreases with distance much faster than do the equivalent dipoles produced by synaptic activation. Second, axonal diameters are generally small compared to dendritic, and so the currents involved are small (and are even smaller for myelinated axons due to saltatory conduction). Third, action potentials are very short and biphasic so tend to cancel due to temporal asynchrony; even a half millisecond offset can result in cancellation whereas waves as long as the P3 (~200ms) will summate even when offset by 100ms. Fourth, axons tend to form tangles resulting in spatial cancellation (rather than palisades like apical dendrites). Fifth, the return currents are close to the primary sinks (especially for action potentials in unmyelinated axons, the most common in the cortex itself) so the dipoles are short and thus weak. There are apparent exceptions, such as the primary somatosensory cortex response to median nerve stimulation [8], but these provide a very weak signal that is only apparent because it is the first cortical response and thousands of trials are averaged. Figure 1. Common Origin of MEG, EEG and BOLD in Active Transmembrane Currents. The excitatory postsynaptic current (EPSC) induced by the opening of ligand- gated channels in the postsynaptic membrane (shown at top at the distal apical shaft of a cortical pyramidal cell), results in an intracellular current (left) which when summated across many cells generates the MEG. The equal but opposite extracellular return current results in the EEG (bottom), and restoring ionic balance through active pumping is a major driving force behind the BOLD response (right). 2 Source estimation Inhibition It has been controversial if inhibitory currents also contribute to M/EEG. A major reason for this doubt has been that GABAa receptors function by permitting Cl- ions to pass, and the reversal potential of chloride (-71 mV) had been thought to be similar to the resting potential of cortical pyramidal cells [9]. Increased Cl- conductance would shunt current arriving at the soma and prevent it from triggering an action potential, thus inhibiting neurons without affecting their membrane potential. Even if this were the case, however, the shunting current would still alter the dipole produced by simultaneous EPSP in the apical dendrites of the same cell by increasing the separation between its poles. This increased dipole length would result in a proportionate increase in dipole strength. Furthermore, the supposedly hyperpolarized state of resting cortical cells was based on measurements in anesthetized animals or slices. More recent data in awake animals find resting potentials of ~-63 mV, i.e., depolarized from the equilibrium potential of Cl- [10]. Finally, GABAb receptors which appear to predominate in associative interactions in the cortex [11] operate mainly via K+ currents, which reverse at -89 mV, far removed from the resting potential. Intrinsic voltage-gated K+ channels are also major contributors to the active currents that have been shown to be major contributors to delta waves [12]. At the circuit level, it appears that inhibition and excitation are largely simultaneous and correlated, especially at the time scale of the P3. The concept of recurrent inhibition holds that a strong excitation would be followed by recurrent inhibition [13]. It had been thought that recurrent inhibition provided a good model for evoked potentials as well as spontaneous EEG. However, it is now appreciated that especially in cortical associative circuits, long-lasting polysynaptic excitation of AMPA and NMDA glutamate receptors are balanced by feedforward GABAb inhibition [14]. Voltage-gated channels Thus far we have mainly discussed the possible contributions to M/EEG of traditional ligand-gated channels that are opened
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